J. Lopez-Gomez, C. Mora-Corral

Algebraic Multiplicity of Eigenvalues of Linear Operators

• Gebundenes Buch

Produktbeschreibung

This book analyzes the existence and uniqueness of a generalized algebraic m- tiplicity for a general one-parameter family L of bounded linear operators with Fredholm index zero at a value of the parameter ? whereL(? ) is non-invertible. 0 0 Precisely, given K?{R,C}, two Banach spaces U and V over K, an open subset ? ? K,andapoint ? ? ?, our admissible operator families are the maps 0 r L?C (? ,L(U,V)) (1) for some r? N, such that L(? )? Fred (U,V); 0 0 hereL(U,V) stands for the space of linear continuous operatorsfrom U to V,and Fred (U,V) is its subset consisting of all Fredholm operators of index zero. From 0 the point of view of its novelty, the main achievements of this book are reached in case K = R, since in the case K = C and r = 1, most of its contents are classic, except for the axiomatization theorem of the multiplicity.

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Produktdetails

• Operator Theory: Advances and Applications 177
• Verlag: Birkhäuser Basel / Springer, Basel
• Artikelnr. des Verlages: 12034413
• 2007
• Seitenzahl: 336
• Erscheinungstermin: 22. Juni 2007
• Deutsch, Englisch
• Abmessung: 250mm x 175mm x 24mm
• Gewicht: 754g
• ISBN-13: 9783764384005
• ISBN-10: 376438400X
• Artikelnr.: 22746943

Autorenporträt

Julián López-Gómez, Universidad Complutense de Madrid, Spain / Carlos Mora-Corral, University of Oxford, UK

Inhaltsangabe

Finite-dimensional Classic Spectral Theory.- The Jordan Theorem.- Operator Calculus.- Spectral Projections.- Algebraic Multiplicities.- Algebraic Multiplicity Through Transversalization.- Algebraic Multiplicity Through Polynomial Factorization.- Uniqueness of the Algebraic Multiplicity.- Algebraic Multiplicity Through Jordan Chains. Smith Form.- Analytic and Classical Families. Stability.- Algebraic Multiplicity Through Logarithmic Residues.- The Spectral Theorem for Matrix Polynomials.- Further Developments of the Algebraic Multiplicity.- Nonlinear Spectral Theory.- Nonlinear Eigenvalues.

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Finite-dimensional Classic Spectral Theory.- The Jordan Theorem.- Operator Calculus.- Spectral Projections.- Algebraic Multiplicities.- Algebraic Multiplicity Through Transversalization.- Algebraic Multiplicity Through Polynomial Factorization.- Uniqueness of the Algebraic Multiplicity.- Algebraic Multiplicity Through Jordan Chains. Smith Form.- Analytic and Classical Families. Stability.- Algebraic Multiplicity Through Logarithmic Residues.- The Spectral Theorem for Matrix Polynomials.- Further Developments of the Algebraic Multiplicity.- Nonlinear Spectral Theory.- Nonlinear Eigenvalues.